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#!/usr/bin/env python
import openturns as ot
import openturns.testing as ott
import math as m
f = ot.SymbolicFunction(
["tau", "alpha"], ["cos(4*tau)*cosh((tau-pi_)/alpha)/cosh(pi_/alpha)"]
)
alpha = 1.36
rho = ot.ParametricFunction(f, [1], [alpha])
cov = ot.StationaryFunctionalCovarianceModel([1.0], [1.0], rho)
print(cov)
tau = 0.1
c = cov([tau])[0, 0]
print("tau=", tau)
print("c=", c)
c_ref = m.cos(4 * tau) * m.cosh((tau - m.pi) / alpha) / m.cosh(m.pi / alpha)
ott.assert_almost_equal(c, c_ref)
assert len(cov.getFullParameter()) == 4, "wrong full parameter"
assert len(cov.getFullParameterDescription()) == 4, "wrong full parameter description"
print(cov.getFullParameter())
print(cov.getFullParameterDescription())
assert len(cov.getActiveParameter()) == 2, "wrong active parameter"
cov.setActiveParameter(range(4))
cov.setParameter([1.0, 0.01, 1.0, 0.5])
assert len(cov.getParameter()) == 4, "wrong parameter"
c = cov([tau])[0, 0]
print("c=", c)
assert c != c_ref, "inactive parameter"
# test discretization
X = ot.Uniform(1, 2).getSample(10)
C = cov.discretize(X)
assert C.getNbRows() == 10, "wrong size"
# thread-safety test
for i in range(1000):
def fun_mixte(X):
xx, z = X
if z == 0:
y = m.sin(7.0 * xx)
else:
y = 2.0 * m.sin(7.0 * xx)
return y
XX_input = ot.Sample(
[
[0.1, 0],
[0.32, 0],
[0.6, 0],
[0.9, 0],
[0.07, 1],
[0.1, 1],
[0.4, 1],
[0.5, 1],
[0.85, 1],
]
)
y_output = ot.Sample(len(XX_input), 1)
for i in range(len(XX_input)):
y_output[i, 0] = fun_mixte(XX_input[i])
def C(s, t):
return m.exp(-4.0 * abs(s - t) / (1 + (s * s + t * t)))
N = 32
a = 4.0
myMesh = ot.IntervalMesher([N]).build(ot.Interval(-a, a))
myCovariance = ot.CovarianceMatrix(myMesh.getVerticesNumber())
for k in range(myMesh.getVerticesNumber()):
t = myMesh.getVertices()[k]
for ll in range(k + 1):
s = myMesh.getVertices()[ll]
myCovariance[k, ll] = C(s[0], t[0])
covModel_discrete = ot.UserDefinedCovarianceModel(myMesh, myCovariance)
f_ = ot.SymbolicFunction(
["tau", "theta", "sigma"],
[
"(tau!=0) * exp(-1/theta) * sigma * sigma + (tau==0) * exp(0) * sigma * sigma"
],
)
rho = ot.ParametricFunction(f_, [1, 2], [0.2, 0.3])
covModel_discrete = ot.StationaryFunctionalCovarianceModel([1.0], [1.0], rho)
covModel_continuous = ot.SquaredExponential([1.0], [1.0])
covarianceModel = ot.ProductCovarianceModel(
[covModel_continuous, covModel_discrete]
)
covarianceModel.discretize(XX_input)
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